There are two distinct uses of "killing it" in your question. The first would be used as such:
You killed it out there! The crowd loved it!
This meaning is more or less explained by the question you linked to:
While its usage to mean "very funny" is partly covered in another question, its usage via idioms like to make a killing to indicate a "large profit" dates back to 1886 (as noted above).
This most likely extended to include individual performances, financial or otherwise.
The second usage is the connotation you describe in this paragraph:
Peculiarly, "killing it" also seems to hold the connotation that it has been done so well, that it is no longer fashionable for anyone else to do a similar performance, because it has 'been killed'. And though I could not find a citation for this, this appears to be implied where I have heard it used in speech.
This is related to the concept of a thing being "dead" and isn't related to the first usage. From the dictionary:
dead: no longer current or prevalent, as in effect, significance, or practice; obsolete: a dead law; a dead controversy
To kill something is to make it dead; in the context of plays and songs they die by phasing out of cultural relevance.
A good example of these are genre killers:
Genre Killer — One order of magnitude greater than Franchise Killer, this is when a work somehow manages to take an entire genre down. A rare and unpredictable phenomenon that can, in extreme cases, cause a genre to become Deader Than Disco.
Of note, these are not necessarily successes. You can kill a genre with a terrible performance. From the TVTropes link, here are two notable examples from Hollywood:
Cutthroat Island was an attempt to revive the swashbuckling adventure movie. Instead it just sunk it farther down into its grave, along with Carolco Studios, the careers of almost everyone involved, and (along with their other collaboration The Long Kiss Goodnight) the marriage of star Geena Davis and director Renny Harlin. The genre was not exactly a thriving one at release, but this made sure no one would even attempt another shot at it. Even after the success of Pirates of the Caribbean, no one seems interested in pirate movies that don't belong to that franchise.
The Jurassic Park films are an example of one series' smash success making it impossible for subsequent films to live up to it. No one has bothered to make a serious dinosaur movie since, and all films and video games that have happened to feature dinosaurs, have, without exception, contain conscious nods to the franchise.